Jordan Gelber (left, with Wayne Knight) is a whirlwind of infectious joy in the title role of this much-improved musical adaptation of a familiar holiday tale. Photo: Joan Marcus

Holiday shows can get away with murder. They have familiar subjects, a captive audience and a limited run, so too often they don’t try as hard as they should.

When it first appeared a couple of years ago, “Elf — The Musical” fit that pattern. The sluggish, saccharine-sweet adaptation of the 2003 Will Ferrell movie wasn’t bad enough to qualify as a lump of coal, but it didn’t make you wish for a return ticket in your stocking.

But there’s been a Christmas miracle on Broadway, because the retooled “Elf” that reopened last night is a startling improvement. Zippier and funnier, the show is now a bona fide treat.

The most obvious and most welcome change is the arrival of Jordan Gelber. A cross between Josh Gad from “The Book of Mormon” and Jonah Hill, Gelber is a whirlwind of infectious joy in the title role.

A 30-year-old naif who was raised on the North Pole by Santa (Wayne Knight) and his diminutive employees, Buddy the Elf doesn’t realize he’s human. When he arrives in New York to search for his real father (Mark Jacoby), he sticks out — not because of his green felt outfit and pointy shoes, but because he’s a relentless optimist who believes in the magic of Christmas.

Gelber (who once played Brian, the would-be comedian and stray human in “Avenue Q”) delivers wicked line readings. “Is he insaaa-aaane?” Buddy wails of his father, the elongated syllable rising and dipping like a roller coaster. He’s no slouch when it comes to physical comedy, either: You won’t soon forget the way he shovels spaghetti into his mouth.

Director/choreographer Casey Nicholaw (“The Book of Mormon”) had the good sense to keep the best performers from the first incarnation — including Beth Leavel as Buddy’s stepmother and Valerie Wright as an office manager — and to find excellent replacements for others.

Leslie Kritzer (“Sondheim on Sondheim”) is her usual sharp self as Jovie, Buddy’s co-worker at a store’s Santaland. As the big man himself, Knight has the same manic undertones he brought to Newman in “Seinfeld.”

In the bright opening number “Happy All the Time,” Santa complains, “When they sing until they’re bluish/Santa wishes he were Jewish.”

That song is new, by the way — just one of the many examples of the tinkering done by Nicholaw and the whole creative team. Some numbers were moved around, Thomas Meehan and Bob Martin’s book flows better, and the pace has picked up.

One wishes the choreography had perked up as well: It could use more pizzazz. Let’s put that on our wish list for the next edition of “Elf.”